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Hello John,
I hope you are fine.
I came across the following question I can’t solve. Could you please advise?The demand curve for a product is P = 24 – 0.004Q. At the current sales price of $10 per unit, demand per week is 3500 units. By how much could the company raise the selling price per unit in order to increase total sales revenue per week, before total sales revenue per week from the product begins to fall into decline?
Thank you!
AnnaThe question wants you to find what price gives maximum revenue.
Maximum revenue occurs when the marginal revenue = 0 (see the free lecture for an explanation as to why).
From the formula sheet, MR = 24 – 0.008Q
If 24 – 0.008Q = 0, then Q = 3,000From the price demand equation, when Q = 3,000, then P = 24 – 0.004×3,000 = $12
Hello John,
Thank you for your reply.
I watched your lectures about optimal pricing for F5 and what I found in Pricing Part 2b is the graph that you drew. It might explain why maximum revenue occurs when marginal revenue equals zero. I’m not sure if I understand it correctly – I have 3 points I’d like to ask about.
1) In dropping the price we come finally to that stage that even if we increase the quantities sold our revenue starts going down. So there is a point in which we cannot get any more marginal revenue (extra revenue)?
2) I understand that this is a marginal revenue per all sales for a given price and not a marginal reveunue per unit?
3) The last thing I wonder about is that. The whole thing about maximum revenue is something different than maximum profit? Max profit occurs when Marginal revenue = Marginal cost and Maximum revenue occurs when Marginal revenue equals 0. So if we take the example from your lecture where:
P= 50 – 0.01Q
VC = $20
Marginal revenue = 50 – 0.02Qthan the maximum profit will occur if we sell 1500 units for $35 p.u. but the maximum revenue will occur if we sell 2500 units for $25p.u.
Please let me know if my thinking is right. Thank you very much.
AnnaThank you for the reply and many thanks for your lectures – they are extremely helpful 🙂
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